A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new bottles arrived in shipments. Which recursive function best represents the number of bottles in the store, given that f (0) = 50?

f (n) = f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.4 + 20, n > 0

f (n) = f (n - 1) ⋅ 0.4 + 20, n > 0

Question

Mathematics

Clare Stuart

15 July, 08:35

A store had 50 bottles of olive oil. Each week, 40% of the olive oil bottles were sold and 20 new bottles arrived in shipments. Which recursive function best represents the number of bottles in the store, given that f (0) = 50?

f (n) = f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.6 + 20, n > 0

f (n) = 50 - f (n - 1) ⋅ 0.4 + 20, n > 0

f (n) = f (n - 1) ⋅ 0.4 + 20, n > 0

+4

Answers (1)

Know the Answer?

Ronnie Yu · Answer 1

f (n) = f (n - 1) ⋅ 0.6 + 20, n > 0

Step-by-step explanation:

Each week 40% of the olive oil bottles were sold. This means, each week 60% of the bottles were left. In addition to these, 20 new bottles arrived in shipments.

So, every week the number of shipments was:

60% of the shipments of previous week + 20

In equation form this can written as:

Shipments in a week = 60% of shipments of previous week + 20

For, nth week we can re-write this equation as:

f (n) = 60% of f (n - 1) + 20

or

f (n) = f (n - 1) ⋅ 0.60 + 20

For example for first week, replace n by 1 to find the number of shipments in week 1 and same goes for next weeks.